Links from Mark Dickinson's website
- Eric Weisstein's World of
Mathematics is an online math encyclopedia with many entries related
to number theory.
- Wikipedia, the free
encyclopedia, has a lot of information on Number theory and much
else besides. See this entry, or
this one, for example.
- The Number
theory section of the Mathematical Atlas
gives an overview of the subject of number theory.
- Chris Caldwell's Prime Pages contain a
great deal of useful, interesting and occasionally silly information
about prime numbers. For example, here's some information about
some (possibly) illegal
- The Great Internet
Mersenne Prime Search (GIMPS) is a distributed computing project
searching for ever larger Mersenne
- PRIMO is a primality proving program by Marcel Martin, based on the
elliptic curve primality proving algorithm. It can be found
along with information about the largest numbers that were proved prime using a
general-purpose primality proving algorithm.
- FactorWorld is
a web site dedicated to integer factorization results and algorithms. It
includes a list of recent factoring records.
RSA Security Inc. Public-Key Cryptography Standards (PKCS) includes recommendations
for practical implementations of the RSA cryptosystem. These
might give you some idea of the gap between the simple mathematical model of
RSA given in class and a real-world implementation.
- The Online
Encyclopedia of Integer Sequences is a gigantic searchable database of
integer sequences. Try looking up the sequence 2,3,7,43,... for example.
- Python is a free, general-purpose
programming language that's very useful for doing basic number theory
calculations, thanks to its interactive interpreter and its unbounded integers.
(I often use it to double-check solutions to numeric homework problems.)
- Pari-GP is a free (as in
beer and speech) calculator for number theory.
- GMP is a library of routines for
arbitrary precision arithmetic. The homepage includes a very useful
- The Math Puzzle site is a great
place to look for recreational mathematics, and has much that's related to
number theory. For example: what's special about the decimal expansion of
1/999998999999? Find the answer, courtesy of Richard Guy,
somewhere on this page.
- The Number
Theory Web pages at Vancouver contain many number
theory-related links and resources.
- Here's some information on
Zi and the
Remainder Theorem, part of a History of Mathematics site at
Simon Fraser University.
- Biographies of mathematicians from
can be found at The
MacTutor History of Mathematics archive at the University of St. Andrews, Scotland.
The Most Common Errors in Undergraduate Mathematics
makes interesting reading, but the sections on Errors in
Communication and Errors in Reasoning ought to be
required reading for this course! See especially the
section on working backwards.